A-stability of Runge-Kutta methods for systems with additive noise
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Numerical stability of both explicit and implicit Runge-Kutta methods for solving ordinary differential equations with an additive noise term is studied. The concept of numerical stability of deterministic schemes is extended to the stochastic case, and a stochastic analogue of Dahlquist'sA-stability is proposed. It is shown that the discretization of the drift term alone controls theA-stability of the whole scheme. The quantitative effect of implicitness uponA-stability is also investigated, and stability regions are given for a family of implicit Runge-Kutta methods with optimal order of convergence.
1980 AMS Subject Classification65L20 (primary) 60H10,34F05 65L07 93E15
Keywords and phrasesNumerical stability Runge-Kutta methods implicit methods stochastic differential equations stochastic stability
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